President Obama offered his prescription Thursday for how to fix Obamacare: Expand it.

In a major speech defending his Affordable Care Act just days before the law's fourth enrollment season starts, Obama laid out a list of measures he said would help expand coverage to the remaining 10 percent of people who still lack insurance. Most of them involve expanding parts of the law, such as convincing holdout states to accept its Medicaid expansion and increasing the subsidies for buying coverage.

"The problem is not that government is too involved in the process," Obama said, speaking at Miami-Dade College in Florida. "The problem is we have not reached everybody and pulled them in."

In past speeches about his healthcare law, Obama has touted its consumer protections and financial assistance for low- and middle-income Americans. But faced with spiking premiums and insurer exits from the marketplaces, the president used his speech Thursday to downplay its influence on the public and list some fixes.

Most people don't get marketplace coverage — just 10 million or so Americans who were previously uninsured, the president noted. And insurance premiums had increased dramatically before the law was passed. But when consumers find their insurance rates are rising, they like to blame him unfairly, Obama said.

"People think 'my insurance rates are going up, it must be Obama's fault,'" Obama told the students.

The president called for a government-funded, public option plan, which he has supported previously, to give shoppers an extra choice in marketplaces with few private options.

"This is not complicated," Obama said. "If no private insurers are providing affordable insurance in an area, the government would step in and offer an affordable plan."

Yet Obama also argued that his healthcare law has improved insurance for nearly all Americans, by requiring insurers to cover more services and banning them from discriminating against patients with preexisting conditions.

And most people don't give the law credit for those benefits, he said.

"So you're getting better quality even if you don't know Obamacare's doing it," he said. "Thanks, Obama,'" he added, prompted laughter in the audience.

It was only after touting the law's benefits and criticizing those who overstate its influence that Obama acknowledged some of its ongoing problems, chiefly that not enough young, healthy people are signing up to keep premiums lower.

"The Affordable Care Act has done what it was designed to do, it gave us affordable healthcare," Obama said. "So what's the problem? Why is there still such a fuss?"

Instead of continually trying to repeal the law, Republicans in Congress should think about how to reach the remaining uninsured Americans, the president urged.

"Just because a lot of the Republican criticism has proven to be false and politically motivated, doesn't mean there aren't some legitimate concerns about how the law is working now, and the main issue has to do with the folks who still aren't getting enough help," he said.

The speech prompted some critics of the healthcare law to air their grievances with it. Republicans pointed to a healthcare plan released over the summer by House Speaker Paul Ryan, which would repeal or gradually phase out most elements of the law while replacing it with a set of ideas conservatives have long championed.

House Budget Committee Chairman Tom Price released a statement criticizing the 2017 premium hikes and saying Obama's speeches about the law won't make healthcare "more affordable or accessible."

"If the American people had a dime for every time the president offered another sales pitch for his disastrous health care law, they might actually be able to afford an Obamacare plan," Price said.